As I understand it you either need to pay for everyone on the booking to select seats now OR wait for BA to give you the free allocation.
Also as long as BA seats the child next to one adult they have met the requirements. It could mean that the other parent is sat elsewhere in the cabin
per this
f you don’t choose your seats in advance, we’ll do our best to seat your family together a few days before your flight departs, from the limited selection of seats available. This might result in your family being split over different rows or across the aisle, however we will make sure each child under 12 is seated with an adult from your booking. Anyone over 12 years is treated as an adult in our system, so we may seat them separately.